The actor was sitting courtside at a New York Knicks game against the Boston Celtics with Galifianakis and Bored to Death series creator Jonathan Ames when he saw Lee make his way towards the trio.
But the revered director was only interested in meeting The Hangover comedian - and Schwartzman was left red-faced as he tried and failed to shake Lee's hand.
He recalls, "We got to go to a Knicks/Celtics play-off game last year and I've never done anything like that. We sat courtside and I went with the real Jonathan Ames, who created the show, and Zach Galifanakis and it was incredible...
"Just over to our left was Spike Lee, who I'm a big fan of... I was really excited and he came over, he had his hand outstretched, and I was like, 'Spike Lee is coming to say hi to me, this is amazing, is this really happening?' So I stuck out my hand and he walked right by me and shook Zach's hand. I was so excited I thought he was going to go this way - Zach, me, Jonathan. But instead, he just shook his hand and walked away and left me there."
But Schwartzman was determined to say hi to Lee and shouted out to him before he could stop himself from acting like a crazed fan.
He says, "It was like a dream, I just yelled, 'Spike!' and he turned around and I said, 'It's Jason!' And he looked really confused and then he walked back and shook my hand and I went, 'And this is Jonathan!' And then he kind of walked away weird and then the Knicks lost!"